Secondly, what kind of panel ? The ROX panel, the wbar panel, the lxpanel or the fbpanel, the jwm panel, the icewm panel ?

For the ROX panel and the lxpanel, you were on the right track : first a right click on the icon, and then there should be an item in the submenu that appeared that says " Remove item" or similar terminology.

AFAIK, the other panels have configuration files that you must "tame" (as in taming a wolf, a cougar or a bear!) However, those panels will not eat you, they will simply test your patience!

There is a little file called "windowmanager" in the /etc directory. If you could tell us the text in that file, please ? It tells the name of the window manager in use.

Also, if you can provide a picture of your desktop or panel, that would help too, in determinig the type of panel.

To make a screen capture:
If you see an icon marked "screen capture" on your desktop, click on it, save the resulting picure and post it here.
If not, go inside the console (also called "terminal") and type "mtpaint -s". That command will create a sreen capture of your desktop. Save it and post it here.

With those informations, we will be able to give you some more focused help.

Yep, all kinds of panels but likely the jwm tray - you can try to do traybuttons (usually on the far left of a typical jwm tray, basically everything to the left of the pager for virtual desktops) in jwmconfig, but I find it may be easier to directly edit the /root/.jwmrc-tray file.

You can 'comment out' a traybutton line by (here's a sample snippet to disable the gexec and showdesktop traybuttons, while leaving the menu traybutton)

If the tray item is a 'swallow' like xload, put the commenting out marks before and after the swallow tags.

If the unwanted icon shows up in jwm's dock (systray that's between the tasklist area and the clock in a typical jwm tray), chances are it's something from /root/Startup - you can disable most of those in bootmanager ~or~ r-click on the file in /root/Startup and untick the exec flags on the property sheet for that file. Restart X to check if you disabled the desired Startup file.